How to create this curved 90-degree-angle quickly
First method:

This one will work only for external Edge Loop and will give ugly ngon, so it's just for the pure knowledge. Better skip to second one.

Select corner vertex, press CTRL+SHIFT+B, move mouse to get desired angle, use scroll to get more vertices. You can tweak it as well in in Tools Panel.



Second method:

This is with proper/clean/nice looking topology.


Make two Loop Cuts trough the surrounding faces - CTRL+R.
Delete corner face.
Select both Edges.
CTRL+E > Bridge Edge Loops.
Set values in Tools Panel or hit F6.




Edit:

I don't know math so maybe someone could elaborate more about what makes smooth corner perfectly 90 degrees. Below some doodling over result by Bridge Edge Loops method.